Let #f(x) = 3x - 4# and #g(x) = x^2 - 2#, what is the value of #f(g(2))# and #f(g(x))#?

Answer 1

#color(blue)(f(g(2))=2)#
#color(white)(.)#
#color(blue)(g(f(x))= -15x+14)#

Assuming you mean: #f(x)=3x-4# #g(x)=x^2-2# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("To determine "f(g(2)))#

#g(2)=2^2-2" " =" "4-2" "=" "2 #

#f(g(2))=3(2)-4" " =" "6-4" "=" "2#

#color(blue)(f(g(2))=2)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("To determine "g(f(x)))#

Given that #f(x)=3x-4# then

#g(f(x))= (3x-4)^2-2#

#g(f(x))= (9x-24x+16)-2#

#color(blue)(g(f(x))= -15x+14)#

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Answer 2

Julia Adams

To find ( f(g(2)) ), substitute ( 2 ) into ( g(x) ) to get ( g(2) ), then substitute the result into ( f(x) ).

( g(2) = 2^2 - 2 = 2 )

( f(g(2)) = f(2) = 3(2) - 4 = 6 - 4 = 2 )

To find ( f(g(x)) ), substitute ( g(x) ) into ( f(x) ).

( f(g(x)) = 3(g(x)) - 4 = 3(x^2 - 2) - 4 = 3x^2 - 6 - 4 = 3x^2 - 10 )

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.